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Period or frequency of a mass with springs in series or parallel

This type of question, asked 7 times: 11 May 2023 S2, 12 May 2024 S1, 25 Apr 2025 S2, 18 Apr 2026 S1, 20 Apr 2026 S1, 12 May 2026 S1, 13 May 2026 S1. All 7 questions below, oldest first.

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  1. Question 1

    11 May 2023 S2

    23
    All the springs in fig. (a), (b) and (c) are identical, each having force constant K. Mass attached to each system is 'm'. If Ta,TbT_a, T_b and TcT_c are the time periods of oscillations of the three systems respectively, then

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  2. Question 2

    12 May 2024 S1

    48
    Four massless springs whose force constants are 2K,2K,K2K, 2K, K and 2K2K respectively are attached to a mass MM kept on a frictionless plane as shown in figure. If mass MM is displaced in horizontal direction the frequency of oscillating system is

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  3. Question 3

    25 Apr 2025 S2

    27
    As shown in the figure, S1S_{1} and S2S_{2} are identical springs with spring constant K each. The oscillation frequency of the mass ' mm ' is ' ff '. If the spring S2S_{2} is removed, the oscillation frequency will become

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  4. Question 4

    18 Apr 2026 S1

    119
    All the springs in fig (a), (b) and (c) are identical, each one having force constant K. Mass m is attached to each system. If TaT_a, TbT_b and TcT_c are the periodic time of oscillations of the three systems in fig (a), (b) and (c) respectively, then

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  5. Question 5

    20 Apr 2026 S1

    118
    Two springs of force constants '2k2k' and 'kk' are connected to a mass 'mm' as shown. Mass is displaced slightly to one side and released. The frequency of oscillation of the two springs-mass system is

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  6. Question 6

    12 May 2026 S1

    119
    A simple harmonic oscillator having four identical springs (as shown in figure) has a time period T1T_1. Another similar simple harmonic oscillator of the same mass mm but the four identical springs with spring constants 2k2k has a time period T2T_2, then T1T2\dfrac{T_1}{T_2} is

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  7. Question 7

    13 May 2026 S1

    119
    S1S_1 and S2S_2 are two identical springs. The frequency of oscillation of mass m is F. If one spring is removed, the frequency will become

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